Lesson 10.1, page 926 Sequences and Summation Notation

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Lesson 10.1, page 926Sequences and Summation
Notation

• Objective To find terms of sequences given the
  nth term and find and evaluate a series.

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DEFINITIONS

• sequence a function in the form of a list,
  whose domain is the set of natural numbers
• term each number in a sequence
• nth term general term

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Fibonacci Sequence

• The Fibonacci Sequence is an infinite sequence
  that begins as follows 1,1, 2, 3, 5, 8, 13,
  21, 34, 55, 89, 144, 233,.
• The first two terms are 1. After that, do you
  notice a pattern?
• Each term is the sum of the two preceding terms.

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Sequence Notation

• Instead of f(x), we write an.
• an f(n) where n is a natural number
• an is the nth term

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Types of Sequences

• Finite Sequence has an end
• Domain is the set 1, 2, 3,4,n n
• Infinite Sequence does not end
• Domain is all natural numbers

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What is a sequence? (re-cap)

• An infinite sequence is a function whose domain
  is the set of positive integers. The function
  values, terms, of the sequences are represented
  by
• Sequences whose domains are the first n integers,
  not ALL positive integers, are finite sequences.

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Find the 1st 3 terms of the sequence

• a) 4, 5/2, 6
• b) 0, 3/2, 2/3
• c) 1, 2, 3
• d) 2, 3/2, 2/3

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See Example 1, page 927.

• Check Point 1 Write the first four terms of the
  sequence whose nth term, or general term is
  given.

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Summation Notation
Ending term
Sigma
Formula to find kth term
Starting term
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Summation Notation

• The sum of the first n terms, as i goes from 1 to
  n is given as
• Example

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See Example 5, page 931.

• Check Point 5 Expand and evaluate the sum